NMR has been a common laboratory technique for over forty years and has become an important tool in formation evaluation. General background of NMR well logging can be found, for example, in U.S. Pat. No. 5,023,551 to Kleinberg et al., which is assigned to the same assignee as the present invention and herein incorporated by reference in its entirety.
NMR relies upon the fact that the nuclei of many chemical elements have angular momentum (“spin”) and a magnetic moment. In an externally applied static magnetic field, the spins of nuclei align themselves along the direction of the static field. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field (e.g., a radio frequency (rf) pulse) that tips the spins away from the static field direction. The angle through which the spins are tipped is given by θ=γB1tP/2, where γ is the gyromagnetic ratio, B1 is the linearly polarized oscillating field strength, and tP is the duration of the pulse. Tipping pulses of 90 and 180 degrees are most common.
After tipping, two things occur simultaneously. First, the spins precess around the direction of the static field at the Larmor frequency, given by ω0=γB0, where B0 is the strength of the static field and γ is the gyromagnetic ratio. For hydrogen nuclei, γ/2π=4258 Hz/Gauss, so, for example, in a frequency of 1 MHz. Second, the spins return to the equilibrium direction according to a decay time, T1, which is known as the spin-lattice relaxation time.
Also associated with the spin of molecular nuclei is a second relaxation time, T2, called the spin-spin relaxation time. At the end of a 90-degree tipping pulse, all the spins are pointed in a common direction perpendicular, or transverse, to the static field, and they all precess at the Larmor frequency. However, due to small fluctuations in the static field induced by other spins or paramagnetic impurities, the spins precess at slightly different frequencies, and the transverse magnetization dephases with a time constant T2.
A standard technique for measuring T2, both in the laboratory and in well logging, uses an RF pulse sequence known as the CPMG (Carr-Purcell-Meiboom-Gill) sequence. As is well known, after a wait time that precedes each pulse sequence, a 90 degree pulse causes the spins to start precessing. Then, at time tE/2, a 180 degree pulse is applied that keeps the spins in the transverse plane but causes the spins, which have been dephasing to refocus at a time tE after the initial 90 degree pulse. By repeatedly manipulating the spins using a series of 180 degree pulses, a series of “spin echoes” appear. The train of echoes is measured and processed to determine the irreversible dephasing, T2.
In rock formations, such as in a borehole environment, T2 for hydrogen-containing fluids (such as water, oil, gas) can have significant contributions due to surface relaxation, bulk relaxation, and diffusion effects, i.e.,                               1                      T            2                          =                              1                          T                              2                ,                surface                                              +                      1                          T                              2                ,                bulk                                              +                      1                          T                              2                ,                diffusion                                                                        (        1        )            Each of these contributions provides some information about the rock formation and/or about the fluid in the rock formation. For example, in a wetting phase, the surface relaxation contribution, T2,surface, dominates the distribution of observed distribution of decay times, ƒ(T2). Spins relax predominantly due to collisions with the grain surface, with the collision rate being inversely proportional to the pore size. This means that the observed relaxation time is roughly proportional to the pore size, i.e., 1/T2,surface=ρ2S/VP, where S is the surface area of the pore, VP is the pore volume, and ρ2 is the surface relaxivity of the rock, a phenomenological parameter that indicates how relaxing the surface is. Thus, for a wetting phase, the observed ƒ(T2) provides information about pore size distribution. In a nonwetting phase, surface relaxation becomes negligible and bulk relaxation, which is related to viscosity, dominates the observed ƒ(T2). Thus, for a nonwetting phase, the observed ƒ(T2) provides information about viscosity.
In a uniform static magnetic field, each spin will experience the same magnetic field strength regardless of its position within the static field, and diffusion will not contribute to the observed ƒ(T2). In a magnetic field gradient, however, each spin will experience different magnetic field strengths as it diffuses through the static field. The Larmor frequencies of the diffusing spins become time dependent, and the series of 180 degree pulses cannot refocus the Spills completely, leading to an additional decay signal. This additional decay signal is proportional to the diffusion coefficient, D, of the fluid and to the square of the gradient strength, g, and the square of the echo spacing, tE i.e.,                               1                      T                          2              ,              diffusion                                      =                              1            12                    ⁢                      γ            2                    ⁢                      g            2                    ⁢                      Dt            E            2                                              (        2        )            Because the diffusion coefficient provides an indication of fluid type, measurement of the diffusion effects on ƒ(T2) can be used as the basis for determining the types of fluids in a rock formation.
Certain NMR measurements of diffusion involve changing the echo spacing, tE, in a standard CPMG sequence, and thus the amount of diffusion the spins undergo between echoes, and then comparing the measured relaxations. FIGS. 1A and 1B generally illustrate this approach. FIG. 1A shows two CPMG sequences with different echo spacings, t1 and t2, where t2 is longer than t1. As the echo spacing increases, the spins diffuse further between echoes, and the measured relaxation times will decrease depending on the diffusion coefficient of the fluid, as given in Equation (2) above. FIG. 1B shows the relaxation distributions, ƒ(T2), for an oil and water determined from the two sets of echoes acquired from the two CPMG sequences illustrated in FIG. 1A. As seen in FIG. 1B, the relaxation distribution with the longer echo spacing, t2, is shifted to lower relaxation times, T2, relative to the relaxation distribution with the shorter echo spacing, t1. The size of the shift is proportional to the size of the diffusion coefficient, as indicated by arrows 1 and 2. The shift of ƒ(T2) for a fluid with a small diffusion coefficient 1, such as heavy oil, is smaller than the shift for a fluid with a larger diffusion coefficient 2, such as water or natural gas.
While such NMR diffusion measurements can be useful, they suffer from a number of drawbacks. For example, for a given acquisition time, the two CPMG sequences will not have the same number of echoes. The CPMG sequence with longer echo spacing will have a smaller number of echoes available, so will suffer from lower signal to noise and lower data quality in general. In addition, relaxation distributions for different fluids often overlap, at least partially, making it difficult to identify shifts of individual relaxation times. In cases where the diffusion coefficients for different fluids are small, the shifts may be difficult to distinguish.
Commonly owned U.S. patent application Ser. No. 09/723,803, incorporated by reference herein in its entirety, discloses a method called diffusion-editing that is useful in separating diffusion and relaxation effect for determining saturation and pore geometry. However, to date, there has been no effective method of determining the wettability (an important parameter that strongly influences the flow of fluids in a porous media) of a porous media wherein the effects of diffusion and relaxation are adequately accounted for.
Accordingly, it is an object of the present invention to provide a method for determining the wettability of a porous media wherein diffusion and relaxation effects are adequately accounted for.